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2011
Density functional theory study on the electronic
structure of n- and p-type doped SrTiO3 at anodic
solid oxide fuel cell conditions
S. Suthirakun
Salai Cheettu Ammal
University of South Carolina - Columbia, [email protected]
G. Xiao
Fanglin Chen
University of South Carolina - Columbia, [email protected]
Hans-Conrad zur Loye
University of South Carolina - Columbia, [email protected]
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Published in Physical Review B, Volume 84, 2011, pages 205102-.
© Physical Review B 2011, American Physical Society
Suthirakun, S., Ammal, S. C., Xiao, G., Chen, F., zur Loye, H.-C., & Heyden, A. (2011). Density functional theory study on the
electronic structure of n- and p-type doped SrTiO3 at anodic solid oxide fuel cell conditions. Physical Review B, 84, 205102.
http://dx.doi.org/10.1103/PhysRevB.84.205102
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Author(s)
S. Suthirakun, Salai Cheettu Ammal, G. Xiao, Fanglin Chen, Hans-Conrad zur Loye, and Andreas Heyden
This article is available at Scholar Commons: http://scholarcommons.sc.edu/eche_facpub/688
PHYSICAL REVIEW B 84, 205102 (2011)
Density functional theory study on the electronic structure of n- and p-type doped SrTiO3
at anodic solid oxide fuel cell conditions
Suwit Suthirakun,1 Salai Cheettu Ammal,1 Guoliang Xiao,2 Fanglin Chen,2 Hans-Conrad zur Loye,3 and Andreas Heyden1,*
1
Department of Chemical Engineering, University of South Carolina, 301 South Main Street, Columbia, South Carolina 29208, USA
Department of Mechanical Engineering, University of South Carolina, 300 South Main Street, Columbia, South Carolina 29208, USA
3
Department of Chemistry and Biochemistry, University of South Carolina, 631 Sumter Street, Columbia, South Carolina 29208, USA
(Received 3 August 2011; published 4 November 2011)
2
The electronic conductivity and thermodynamic stability of mixed n-type and p-type doped SrTiO3 have
been investigated at anodic solid oxide fuel cell (SOFC) conditions using density functional theory (DFT)
calculations. In particular, constrained ab initio thermodynamic calculations have been performed to evaluate the
phase stability and reducibility of various Nb- and Ga-doped SrTiO3 at synthesized and anodic SOFC conditions.
The density of states (DOS) of these materials was analyzed to study the effects of n- and p-doping on the
electronic conductivity. In agreement with experimental observations, we find that the transformation from 20%
Nb-doped Sr-deficient SrTiO3 to a non-Sr-deficient phase occurs at high temperature and low oxygen partial
pressure, which leads to a significant improvement in electronic conductivity. A mixed ionic/electronic conductor
is obtained when doping 20% Nb-doped SrTiO3 with small amounts of Ga (10%) in a reducing environment and
high temperature. Doping with higher concentrations of Ga, e.g., 20%, diminishes the electronic conductivity of
the material. These findings suggest that independent of the specific dopant, mixed ionic/electronic conductivity
can be obtained in perovskite oxides under reducing conditions and high temperatures by doping the B-site with
small amounts of both n-type and p-type dopants.
DOI: 10.1103/PhysRevB.84.205102
PACS number(s): 71.20.Ps, 72.80.Jc
I. INTRODUCTION
Although Ni-supported yttria-stabilized zirconia (Ni/YSZ)
cermet exhibits very good catalytic activity for fuel oxidation
in solid oxide fuel cells (SOFCs), it is easily poisoned by
small amounts of sulfur impurities in the fuel gas.1 Moreover,
it is prone to sintering2–4 and coking when exposed to
hydrocarbon fuels.5 As a result, exploring alternative SOFC
anode materials to replace Ni/YSZ has become a crucial
subject for the development of SOFC technology. Of the novel
anode catalysts, perovskite-based materials have been shown
to satisfy most intrinsic SOFC anode requirements such as high
mixed ionic/electronic conductivity, good catalytic activity,
and high thermodynamic stability at anodic conditions.6–12
Furthermore, perovskite-based materials possess high resistance to sulfur impurities13–15 and coke formation5,6,16,17 since
both sulfur and carbon species can easily be oxidized at the
surface of the perovskite oxide.18
Among the numerous perovskite systems that have been
explored, SrTiO3 -based perovskites have been widely used
as alternative SOFC anode materials.8,9,14,19 Indeed, several
research groups have reported that SrTiO3 -based perovskites
exhibit some advantages over Ni/YSZ anode catalysts, such
as promising mixed ionic/electronic conductivity, adequate
thermodynamic stability in a wide range of oxygen partial
pressure, and tolerance to sulfur impurities as well as coke
formation.9,13–15 Moreover, it has been found that yttriumdoped SrTiO3 (SYT) possesses a thermal expansion coefficient
compatible with that of YSZ and Lanthanum Strontium
Gallium Magnesium Oxide (LSGM)-based electrolytes.9
However, stoichiometric SrTiO3 is a band insulator with
a band gap of 3.2 eV.20 Therefore, various dopants have
been introduced to improve the electronic conductivity of this
material. It is well known that doping the material with either
n- or p-type dopants can enhance the degree of electronic
1098-0121/2011/84(20)/205102(9)
conduction.21–25 For example, the transformation from an
insulating state to a metallic state has been observed when
doping SrTiO3 with n-type impurities such as La, Y, and
Nb.14,26–28 In addition theoretical studies have suggested that
substituting Ti with n-type dopants can shift the Fermi level
into the conduction band making the system metallic.23,29
It is well known that the substitution of n-type dopants in
the SrTiO3 lattice generates a defect with an effective positive
charge in the host lattice. Overall electroneutrality of the lattice
can be achieved by two different mechanisms, namely, electronic compensation and cation-vacancy compensation.30–32
At low oxygen chemical potential, the formal charges of n-type
dopants are electronically compensated by creating conduction
electrons that travel along the Ti–O–Ti bridge where Ti
remains mixed-valent Ti3+ /Ti4+ .33 This electron-transferring
process is considered to be the origin of the electronic
conductivity of the material.34 On the other hand at higher
oxygen chemical potential the excess positive charge can be
compensated by generating Sr2+ cation vacancies.35 This type
of electron compensation provides no conduction electrons
and there is no improvement in electronic conductivity. For
example, Kolodiazhnyi and Petric28 found that TiO2 and
niobium oxide second phases were formed when sintering the
Sr1−x/2 Ti1−x Nbx O3 (x = 0.17) at low oxygen partial pressure
and high temperature. This transformation can be expressed
with the following equation:
Sr1− x2 Ti1−x Nbx O3 → Sr1− x2 Ti1−x−y Nbx−y O3−4y
+ yTiO2 + yNbO2 ,
(1)
where y < x 0.2.
Furthermore, they observed a very high electronic conductivity of Sr0.9 Ti0.8 Nb0.2 O3 and Sr0.88 Y0.08 TiO3 when these
samples were sintered in forming gas.28
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©2011 American Physical Society
SUWIT SUTHIRAKUN et al.
PHYSICAL REVIEW B 84, 205102 (2011)
In contrast to n-type doping, p-type dopants create an
effective negative charge in the lattice. One way to neutralize
the charge is introducing oxygen vacancies in the lattice. This
mechanism of charge neutralization can take place at moderate
oxygen chemical potentials and does generally not lead to
improved electronic conductivity since there is no transfer
of charges or electrons into the lattice. However, lowering
the oxygen chemical potential can result in more oxygen
vacancies, leading to an excess electron density in the lattice.
The reduction reaction takes place at the surface of the material
and delivers electrons to the lattice,36
◦◦
1
O×
O 2 O2 (g) + VO + 2e .
(2)
These conduction electrons can often be transferred to
neighboring atoms such as Ti, which can be mixed-valent
Ti3+ /Ti4+ . As a result, the electrical conductivity of the
material is again improved.
The addition of p-type impurities not only improves the
electronic conductivity but also enhances the ionic conductivity by increasing the reducibility and number of oxygen
vacancies in the material. Furthermore, the amount of available
oxygen vacancies plays an essential role in the enhancement
of the oxide ion diffusivity (DO2 ) in the lattice as evidenced
by the following equation:37
DO2 = β[VÖ ]a 2 ν0 e−Hm /RT ,
(3)
where [VÖ ] is the concentration of mobile vacancies; a is the
cell parameter; ν0 is a characteristic lattice frequency; Hm
is the enthalpy of vacancy migration; T is temperature; R is
the ideal gas constant; and β = 6z f eSm /R is a function of the
number of equivalent near-neighbor sites z, the entropy of ion
migration Sm , and a correction factor f (≈1). It is noted
that the mobile vacancy concentration is usually smaller than
the stoichiometric concentration due to vacancy trapping or
vacancy ordering.38,39
Recently, various research groups reported that the catalytic
activity and mixed ionic/electronic conductivity of n-type
doped SrTiO3 can be modified by B-site doping with p-type
impurities such as Sc, Mn, and Ga.40 For example, Li et al.41,42
suggested that doping with Sc and Co at the B-site of
La0.3 Sr0.7 TiO3 can improve its ionic conductivity. Similarly,
Xiao et al.43 and Neagu and Irvine44 proposed a similar
doping strategy to improve the conductivity of n-type doped
SrTiO3 by enhancing bulk oxide ion mobility. In particular,
they studied the effects of Ga dopants on the reducibility and
conductivity of n-type doped SrTiO3 systems by varying the
concentration of Ga. They found that Ga doping promotes fast
reduction and improves the phase stability of the material in
an oxidizing environment. Impressive improvements in total
conductivity were observed when doping with small amounts
of Ga.
It is the objective of this theoretical study to further
investigate the effect of concurrent n- and p-doping on the
number of oxygen vacancies and the electronic conductivity
of SrTiO3 perovskites. In particular, we performed density
functional theory (DFT) calculations of Nb- and Ga-doped
SrTiO3 and analyzed the electronic structure of the resulting
materials. To evaluate the thermodynamic stability of doped
SrTiO3 phases at synthesized and anodic SOFC conditions, we
FIG. 1. (Color online) (a) Unit cell of SrTiO3 perovskite oxide.
(b) Density of states of stoichiometric SrTiO3 with calculated band
gap of 1.80 eV.
furthermore performed constrained ab initio thermodynamic
simulations.
II. COMPUTATIONAL DETAILS
A. Crystallographic data of SrTiO3
Stoichiometric SrTiO3 develops an ideal cubic perovskite
structure at room temperature with Pm3m space group. The
structural phase transition from cubic to tetragonal and to
orthorhombic occurs at 110 and 65 K, respectively.45 The cubic
unit cell includes one molecular unit of SrTiO3 . As shown in
Fig. 1(a), the structure contains 12-coordinated strontium ions
occupying corner positions of the cube, whereas the titanium
ion, at the center of the cubic cell, is surrounded by six
oxygen ions forming a TiO6 octahedral unit. The octahedral
units are connected by a sharing Ti–O–Ti bridge, forming a
three-dimensional framework.
B. Computational method
To investigate the bulk electronic properties of stoichiometric and doped SrTiO3 , we initially optimized the lattice
parameter of the SrTiO3 unit cell and created a 100 atom
supercell containing twenty unit cells (5 × 2 × 2). To
generate doped structures we replaced B-site cations (Ti)
with various amounts of n-type (Nb) and p-type (Ga)
dopants. Substitution of two Ti atoms with two dopants
yields 10% B-site doped SrTiO3 , etc. In order to better
understand the charge compensation mechanism in n- and
p-type doped systems, both A-site deficient and reduced
structures were created by generating strontium vacancies and
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DENSITY FUNCTIONAL THEORY STUDY ON THE . . .
PHYSICAL REVIEW B 84, 205102 (2011)
oxygen vacancies, respectively. In this study we considered
up to two strontium vacancies and three oxygen vacancies
in each structure. For all doped structures, we employed the
lattice parameter of 20% Nb-doped SrTiO3 and tried close
to all ion position possibilities to identify the lowest energy
structures.
All calculations performed for this study are based on
the plane wave DFT implementation of the Vienna Ab initio
Simulation Package (VASP 4.6).46,47 We used the projectoraugmented wave (PAW) method to represent the inner core
potentials46 and treated the Sr 4s4p5s, Ti 3d4s, O 2s2p, Nb
4p5s4d, and Ga 4s4p as valence electrons. The cutoff of the
kinetic energy was set for all calculations to 400 eV. Exchange
correlation is described within the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE)
functional.48 All calculations are spin-polarized, and Brillouin
zone integration was performed with a 2 ×5 × 5 MonkhorstPack k-point mesh.49 For density of state (DOS) calculations
we used a 4 × 10 × 10 k-mesh. In all structure optimizations,
all atoms are fully relaxed until the Hellman-Feynman forces
are less than 0.02 eV Å−1 .
Our calculated stoichiometric SrTiO3 bulk unit cell has an
optimized lattice constant of 3.948 Å, which is in reasonable
agreement to the experimental value of 3.90 Å.50 The optimized supercell of 20% Nb-doped SrTiO3 exhibits only a
very small change in lattice parameters (3.949 Å) to that of
stoichiometric SrTiO3 . Computations predict a Sr-O and Ti-O
bond distance of 2.792 and 1.974 Å, respectively. As illustrated
in Fig. 1(b), the DOS of stoichiometric SrTiO3 exhibits
insulating behavior with a band gap of 1.80 eV. It should be
noted that while DFT within the GGA approximation is known
to underestimate band gaps, several studies showed excellent
agreement in the predicted electronic behavior of doped
oxides computed by DFT within the GGA approximation and
experimental observation.51–53
III. RESULTS AND DISCUSSION
In this work we are most interested in the electronic
properties of n- and p-type doped SrTiO3 . Kolodiazhnyi
and Petric28 observed experimentally that Sr0.9 Ti0.8 Nb0.2 O3
exhibits a very high conductivity at low oxygen chemical
potential, and Xiao et al.43 suggested that the reducibility of
this material can be promoted by doping with a certain (small)
amount of p-type dopant (Ga). Therefore, we performed three
different sets of calculations based on the concentration of
B-site dopants, i.e., 20% Nb-doped SrTiO3 , 10% Ga- and
20% Nb-doped SrTiO3 , and 20% Ga- and 20% Nb-doped
SrTiO3 . In this way we can systematically study the effect
of Ga (p-type) doping on Nb (n-type) doped SrTiO3 on the
reducibility/phase stability and electronic conductivity/DOS
of the resulting materials.
For all structures we first performed constrained ab initio
thermodynamic calculations to evaluate the relative thermodynamic stability of the systems. This ab initio thermodynamic
approach allows us to calculate the free energy of different
systems as a function of oxygen chemical potential, i.e.,
temperature and oxygen partial pressure, and to construct
phase diagrams. The reaction energies of the most dominant
structures in the phase diagrams are summarized in Table I.
Next, the DOS related to the most dominant structures in the
phase diagram were evaluated and analyzed with respect to the
relative electronic conductivity. Figures of all structures found
most stable at a specific oxygen chemical potential and the
stoichiometry and reaction energy of all structures considered
can be found in the supporting information.54
TABLE I. Summary of reaction energies used in constrained ab initio thermodynamic calculations.
Phase diagram
Nb2 O5 /NbO2
20% Nb-doped
SrTiO3 with SrO-rich phase
20% Nb-doped
SrTiO3 with
TiO2 /niobium oxiderich phases
Reaction
Nb2 O5 → 2NbO2 + 1/2O2
Sr20 Ti16 Nb4 O60 + 1/2O2 → Sr19 Ti16 Nb4 O60 + SrO
Sr20 Ti16 Nb4 O60 + O2 → Sr18 Ti16 Nb4 O60 + 2SrO
19Sr18 Ti16 Nb4 O60 → 18Sr19 Ti16 Nb4 O60 + 16TiO2 + 2Nb2 O5 + 9O2
10Sr18 Ti16 Nb4 O60 → 9Sr20 Ti16 Nb4 O60 + 16TiO2 + 2Nb2 O5 + 9O2
19Sr18 Ti16 Nb4 O60 → 18Sr19 Ti16 Nb4 O60 + 16TiO2 + 4NbO2 + 10O2
10Sr18 Ti16 Nb4 O60 → 9Sr20 Ti16 Nb4 O60 + 16TiO2 + 4NbO2 + 10O2
E (eV)
3.71
−1.94
−3.49
2.58
5.24
2.97
5.98
Sr20 Ti14 Nb4 Ga2 O60 + 1/2O2 → Sr19 Ti14 Nb4 Ga2 O60 + SrO
Sr20 Ti14 Nb4 Ga2 O60 → Sr20 Ti14 Nb4 Ga2 O59 + 1/2O2
Sr20 Ti14 Nb4 Ga2 O60 → Sr20 Ti14 Nb4 Ga2 O58 + O2
Sr20 Ti14 Nb4 Ga2 O60 → Sr20 Ti14 Nb4 Ga2 O57 + 3/2O2
−1.74
4.54
9.01
14.16
10% Ga- and
20% Nb-doped
SrTiO3 with
TiO2 /Ga2 O3 /niobium
oxide-rich phases
19Sr18 Ti14 Nb4 Ga2 O60 → 18Sr19 Ti14 Nb4 Ga2 O60 + 14TiO2 + 2Nb2 O5 + Ga2 O3 + 19/2O2
10Sr18 Ti14 Nb4 Ga2 O60 → 9Sr20 Ti14 Nb4 Ga2 O60 + 14TiO2 + 2Nb2 O5 + Ga2 O3 + 19/2O2
10Sr18 Ti14 Nb4 Ga2 O60 → 9Sr20 Ti14 Nb4 Ga2 O59 + 14TiO2 + 2Nb2 O5 + Ga2 O3 + 14O2
10Sr18 Ti14 Nb4 Ga2 O60 → 9Sr20 Ti14 Nb4 Ga2 O58 + 14TiO2 + 2Nb2 O5 + Ga2 O3 + 37/2O2
10Sr18 Ti14 Nb4 Ga2 O60 → 9Sr20 Ti14 Nb4 Ga2 O57 + 14TiO2 + 2Nb2 O5 + Ga2 O3 + 23O2
−1.29
1.28
5.37
9.39
14.03
20% Ga- and
20% Nb-doped
SrTiO3
10Sr18 Ti12 Nb4 Ga4 O60 → 9Sr20 Ti12 Nb4 Ga4 O60 + 12TiO2 + 2Nb2 O5 + 2Ga2 O3 + 10O2
10Sr18 Ti12 Nb4 Ga4 O60 → 9Sr20 Ti12 Nb4 Ga4 O59 + 12TiO2 + 2Nb2 O5 + 2Ga2 O3 + 29/2O2
10Sr18 Ti12 Nb4 Ga4 O60 → 9Sr20 Ti12 Nb4 Ga4 O58 + 12TiO2 + 2Nb2 O5 + 2Ga2 O3 + 19O2
10Sr18 Ti12 Nb4 Ga4 O60 → 9Sr20 Ti12 Nb4 Ga4 O57 + 12TiO2 + 2Nb2 O5 + 2Ga2 O3 + 47/2O2
−2.81
1.21
5.21
9.82
10% Ga- and 20%
Nb-doped SrTiO3
with
SrO-rich phase
205102-3
SUWIT SUTHIRAKUN et al.
PHYSICAL REVIEW B 84, 205102 (2011)
A. Electronic structure and phase diagram of 20%
Nb-doped SrTiO3
In this set of calculations we substituted four Ti atoms with
four Nb atoms in the 5 × 2 × 2 supercell to obtain a model for
20% Nb-doped SrTiO3 (Sr20 Ti16 Nb4 O60 or SrTi0.8 Nb0.2 O3 ). In
addition we generated structures with one or two Sr vacancies
to create partial (5%) A-site deficient (Sr19 Ti16 Nb4 O60 or
Sr0.95 Ti0.8 Nb0.2 O3 ) and full (10%) A-site deficient 20% Nbdoped SrTiO3 (Sr18 Ti16 Nb4 O60 or Sr0.9 Ti0.8 Nb0.2 O3 ) model
structures, respectively. From the configuration of the most
stable structures, we observe that Nb impurities prefer to be as
far apart as possible due to the repulsion of the extra electrons
from the Nb5+ cations that can be transferred to neighboring
Ti atoms that are mixed-valent Ti3+ /Ti4+ . In contrast when
there are Sr vacancies in the structure, Nb prefers to stay close
to the vacancies since the charges originating from the Nb
atoms can be compensated by the absence of the Sr2+ cations.
Moreover, it was found that the Sr-vacancy sites stay apart
from each other in structures with more than one vacancy (see
supplementary material for the structures, Fig. S1).54
Constrained ab initio thermodynamic calculations of 20%
Nb-doped SrTiO3 systems were performed to determine the
phase stability of these structures at various temperatures and
oxygen partial pressures. We employed two different types of
calculations based on the main products that were generated
when the phase transition occurred. First, we calculated the
free energies of 20% Nb-doped SrTiO3 with a SrO-rich second
phase experimentally obtained by cooling SrTi0.8 Nb0.2 O3 ,
x
Sr20 Ti16 Nb4 O60 + O2
2
→ Sr20−x Ti16 Nb4 O60 + xSrO,
(4)
where x represents the number of Sr-vacancy sites in the
structure (x = 1,2), and free energies are given by
G = ESr−vacancy + xESrO − Efull
− x[EO + μO (T ,P )],
FIG. 2. (Color online) Calculated phase diagram of Nb2 O5 /NbO2 .
Differently shaded areas mark the stability regions of various
structures for a given temperature and partial pressure of oxygen.
The hatched area decribes possible changes in the phase diagram if
computed reaction energies shown in Table I are off by ±0.2 eV
(our estimated error bar). Green and red areas symbolize stability of
Nb2 O5 and NbO2 , respectively.
difference are insignificant.58–60 Also, the pressure dependence
of μO (T ,P ) is obtained assuming that the gas phase is
ideal,59
1
P
μO (T ,P ) =
. (7)
μO2 (T ,P 0 ) + kB T ln
2
P0
Next, we employed the same ab initio thermodynamic
approach to investigate the thermodynamic stability of 20%
Nb-doped SrTiO3 with TiO2 and niobium oxide-rich second
phases that can experimentally be obtained by heating Srdeficient 20% Nb-doped SrTiO3 . Considering that Nb2 O5
can be reduced to NbO2 in a reducing environment at high
temperature,61 we first performed ab initio thermodynamic
calculations of the Nb2 O5 /NbO2 system
(5)
Nb2 O5 → 2NbO2 + 12 O2 ,
(8)
with ESr−vacancy being the DFT-calculated electronic energy
of the structure with Sr-vacancy, Efull is the DFT-calculated
electronic energy of the structure without Sr-vacancy, ESrO
is the DFT-calculated electronic energy of the SrO lattice,
and EO is half of the energy of an oxygen molecule EO2 ,
which is obtained from the H2 O splitting reaction using the
experimental reaction energy and calculated DFT energies of
H2 and H2 O in the gas phase,55,56
DFT
− EH2 + EHZPE
EO2 = 2 EHDFT
+ EHZPE
2O
2O
2
− Ehof − EOZPE
,
(6)
2
and Fig. 2 illustrates that at low temperature Nb2 O5 is the
dominant phase whereas the NbO2 phase predominates at
higher temperatures.
In the following we performed ab initio thermodynamic
calculations of the Nb-doped SrTiO3 system according to
the dominant phase in the Nb2 O5 /NbO2 phase diagram, i.e.,
whenever the Nb2 O5 phase is preferred we calculate the free
energies of the system according to Eq. (9),
where E ZPE is the experimental zero point energy,57 Ehof
is the experimental heat of formation of a gas-phase H2 O
molecule,57 and E DFT is the energy calculated with PBE
functional. The chemical potential of O, which includes the
temperature- and pressure-dependent free energy contributions
of the O2 molecule, is described by μO (T ,P ) and has been
calculated from first principles and the rotational, translational,
and vibrational partition functions of the O2 molecule. We note
that we neglect all zero point energies in Eq. (5) and assume
that entropic contributions from the solids to the free energy
(9)
(20 − x)Sr18 Ti16 Nb4 O60
→ 18Sr20−x Ti16 Nb4 O60 + (32 − 16x)TiO2
+ (4 − 2x)Nb2 O5 + (18 − 9x)O2
and whenever NbO2 is preferred, we calculate the free energies
of the system according to Eq. (10),
(20 − x)Sr18 Ti16 Nb4 O60
→ 18Sr20−x Ti16 Nb4 O60 + (32 − 16x)TiO2
+ (8 − 4x)NbO2 + (20 − 10x)O2 ,
(10)
where x is the number of Sr vacancies with x = 0,1.
Figure 3 shows the calculated phase diagrams of 20%
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PHYSICAL REVIEW B 84, 205102 (2011)
FIG. 3. (Color online) Calculated phase diagram of 20% Nbdoped SrTiO3 with (a) SrO-rich phase and (b) TiO2 /niobium oxiderich phases. Differently shaded areas mark the stability regions of
various structures for a given temperature and partial pressure of
oxygen. The hatched area decribes possible changes in the phase
diagram if computed reaction energies shown in Table I are off
by ±0.2 eV (our estimated error bar). Green, yellow, and red
areas symbolize stability of Sr0.9 Ti0.8 Nb0.2 O3 , Sr0.95 Ti0.8 Nb0.2 O3 , and
SrTi0.8 Nb0.2 O3 , respectively.
Nb-doped SrTiO3 with SrO-rich second phase and TiO2
and niobium oxide-rich second phases. The phase transformation from 10% Sr-deficient (Sr0.9 Ti0.8 Nb0.2 O3 ) to 5%
Sr-deficient (Sr0.95 Ti0.8 Nb0.2 O3 ) to non-Sr-deficient structures
(SrTi0.8 Nb0.2 O3 ) occurs with increasing temperature and
decreasing oxygen partial pressure. We note that an oxygen
deficient structure is thermodynamically unstable in the
considered temperature and oxygen partial-pressure range.
The electronic conductivity of these materials can, to a first
approximation, be analyzed from their electronic structures.
As illustrated in Fig. 4(a), the DOS of a 10% Sr-deficient
material (Sr0.9 Ti0.8 Nb0.2 O3 ) exhibits insulating behavior with a
band gap of 1.80 eV. The charges from the four Nb dopants are
compensated by the presence of two Sr vacancies. The DOS
of the 5% Sr-deficient structure (Sr0.95 Ti0.8 Nb0.2 O3 ) shows
a slight improvement in electronic conductivity [Fig. 4(b)].
The Fermi energy shifts inside the conduction band with two
conduction electrons per supercell below the Fermi level. An
even greater improvement in the electronic conductivity occurs
when the material is fully electronically compensated. As depicted in Fig. 4(c), the DOS of 20% Nb-doped SrTiO3 with no
Sr vacancies (SrTi0.8 Nb0.2 O3 ) exhibits metallic character with
four delocalized electrons at the Fermi level. Calculated band
structures of this material shown in the supporting information
(Fig. S5) confirm the metallic behavior of this material.54
FIG. 4. Density of states of (a) Sr0.9 Ti0.8 Nb0.2 O3 ,
(b) Sr0.95 Ti0.8 Nb0.2 O3 , and (c) SrTi0.8 Nb0.2 O3 . Fermi energy is set
to zero on energy scale. Numbers of electrons shown in the figure
indicate the integrated number of electrons per supercell for the
specified DOS area, i.e., states below the Fermi level.
It is interesting to note that the simulation results are in
agreement with experimental observations from Kolodiazhnyi
and Petric.28 They reported that the transformation of cation
vacancy compensated materials to electronically compensated
materials (and corresponding change in electronic conductivity) occurred when the materials were equilibrated at high
temperature and low oxygen partial pressure. This condition
corresponds to anodic SOFC conditions with temperatures
between 1000 and 1200 K and oxygen partial pressures in
the range of 10−20 bar.
B. Electronic structure and phase diagram of 10% Ga- and
20% Nb-doped SrTiO3
Substitution of two Ti atoms with two Ga atoms in our
20% Nb-doped SrTiO3 model leads to 10% Ga- and 20%
Nb-doped SrTiO3 . The presence of Sr and oxygen vacancies
in the structure was investigated in a similar manner, as
described previously. It is found that Ga atoms prefer to be
next to Nb atoms since the extra electron from the Nb dopant
can be compensated by the electron hole generated from the
Ga dopant (see also supporting information, Fig. S2).54 At
high temperatures and low oxygen partial pressure oxygen
vacancies start to form. The first oxygen vacancy is created by
removing an oxygen atom from the Ga–O–Ti bridge forming
GaO5 units, whereas the second vacancy is positioned next to
the same Ga atom generating a GaO4 unit. Upon removal of
the third oxygen atom another GaO5 unit is formed in our unit
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SUWIT SUTHIRAKUN et al.
PHYSICAL REVIEW B 84, 205102 (2011)
FIG. 5. (Color online) Calculated phase diagram of 10%
Ga- and 20% Nb-doped SrTiO3 with (a) SrO-rich phase and
(b) TiO2 /Ga2 O3 /niobium oxide-rich phases. Differently shaded areas mark the stability regions of various structures for a given
temperature and partial pressure of oxygen. The hatched area
decribes possible changes in the phase diagram if computed reaction
energies shown in Table I are off by ±0.2 eV (our estimated
error bar). Blue, green, yellow, and red areas symbolize stability of
Sr0.95 Ti0.7 Nb0.2 Ga0.1 O3 , SrTi0.7 Nb0.2 Ga0.1 O3 , SrTi0.7 Nb0.2 Ga0.1 O2.9 ,
and SrTi0.7 Nb0.2 Ga0.1 O2.85 , respectively. The hatched violet area
symbolizes the possible stability of a SrTi0.7 Nb0.2 Ga0.1 O2.95 phase.
cell. It is noteworthy that we find structures with neighboring
Ga atoms to be significantly less stable.
Figures 5(a) and 5(b) illustrate the phase diagram for 10%
Ga- and 20% Nb-doped SrTiO3 as a function of temperature
and partial pressure of oxygen corresponding to the formation
of SrO and TiO2 /Ga2 O3 /niobium oxide-rich second phases,
respectively. In the presence of Ga we find that the reduced
structures (SrTi0.7 Nb0.2 Ga0.1 O2.95 , SrTi0.7 Nb0.2 Ga0.1 O2.90 , and
SrTi0.7 Nb0.2 Ga0.1 O2.85 ) are stable in the studied high temperature and low oxygen partial pressure range. The existence
of a reduced structure indicates that Ga doping improves the
reducibility of the materials, as previously reported in Neagu
and Irvine’s work.44 More interestingly, Ga and Nb dopants
do not seem to compensate each other with respect to electronic conductivity. Figure 6 illustrates the DOS of the most
important structures. While Sr0.95 Ti0.7 Nb0.2 Ga0.1 O3 exhibits
insulating behavior with a band gap of 1.80 eV (the charges
from the Nb dopants are compensated by the Sr vacancies
and Ga dopants), SrTi0.7 Nb0.2 Ga0.1 O3 , SrTi0.7 Nb0.2 Ga0.1 O2.95 ,
SrTi0.7 Nb0.2 Ga0.1 O2.90 , and SrTi0.7 Nb0.2 Ga0.1 O2.85 exhibit
metallic behavior with up to four conduction electrons at
the Fermi level (the same number as in the absence of Ga).
In SrTi0.7 Nb0.2 Ga0.1 O3 , the two Ga atoms in the supercell
FIG. 6. Density of states of (a) Sr0.95 Ti0.7 Nb0.2 Ga0.1 O3 , (b) SrTi0.7
Nb0.2 Ga0.1 O3 , (c) SrTi0.7 Nb0.2 Ga0.1 O2.95 , (d) SrTi0.7 Nb0.2 Ga0.1 O2.9 ,
and (e) SrTi0.7 Nb0.2 Ga0.1 O2.85 . Fermi energy is set to zero on energy
scale. Numbers of electrons shown in the figure indicate the integrated
number of electrons per supercell for the specified DOS area, i.e.,
states in the band gap and states below the Fermi level.
compensate for two of the Nb atoms, leaving the remaining two
Nb atoms to contribute two conduction electrons at the Fermi
level [Fig. 6(b)]. In SrTi0.7 Nb0.2 Ga0.1 O2.95 , one oxygen atom
connected to a Ga atom is removed, compensating the hole
doping effect of two Ga atoms. Thus, we see the effect of 20%
Nb doping in this structure [Fig. 6(c)]. In SrTi0.7 Nb0.2 Ga0.1 O2.9
and SrTi0.7 Nb0.2 Ga0.1 O2.85 , the electrons generated by creating
further oxygen vacancies are localized mainly on the Ga atoms,
and an extra peak is observed in the DOS [Figs. 6(d) and
6(e)] between the valence band and the conduction band.
A partial density of states (PDOS) analysis and electron
density integration for SrTi0.7 Nb0.2 Ga0.1 O2.9 , as illustrated in
Fig. 7(a), shows that there are two electrons in this peak,
which predominantly contains contributions from the oxygen
PDOS. We see no reason for these two electrons to be
delocalized and believe that these states do not contribute
to the electronic conductivity of the material. We find a
qualitatively similar picture for the four electrons in the
extra peak in the band gap of SrTi0.7 Nb0.2 Ga0.1 O2.85 . This
observation is in agreement with previous computational and
experimental results that the electrons from oxygen vacancies
are often localized and have little contribution to the electronic
conductivity of the materials.62,63 Next, Fig. 7(b) shows the
PDOS of SrTi0.7 Nb0.2 Ga0.1 O2.9 below the Fermi level and
confirms that these states are primarily from mixed-valent
Ti3+ /Ti4+ that contribute to electronic conduction. A similar
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PHYSICAL REVIEW B 84, 205102 (2011)
FIG. 8. (Color online) Calculated phase diagram of 20% Gaand 20% Nb-doped SrTiO3 . Differently shaded areas mark the
stability regions of various structures for a given temperature and
partial pressure of oxygen. The hatched area decribes possible
changes in the phase diagram if computed reaction energies shown
in Table I are off by ±0.2 eV (our estimated error bar). Blue,
yellow, and red areas symbolize stablity of SrTi0.6 Nb0.2 Ga0.2 O3 ,
SrTi0.6 Nb0.2 Ga0.2 O2.9 , and SrTi0.6 Nb0.2 Ga0.2 O2.85 , respectively. The
hatched green area symbolizes the stability of a SrTi0.6 Nb0.2 Ga0.2 O2.95
phase.
FIG. 7. (Color online) Partial density of states of (a) the gap states
between the valence and conduction band and (b) the states below
the Fermi level in SrTi0.7 Nb0.2 Ga0.1 O2.9 .
behavior is observed for all structures studied with states below
the Fermi level.
To conclude, further doping of 20% Nb-doped SrTiO3 with
10% Ga leads to a comparable degree of electronic conductivity to that of only 20% Nb-doped SrTiO3 under anodic
SOFC conditions. Further, Ga promotes ionic conductivity
by enhancing the reducibility of the material. These results
support the experimental observations reported by several
groups43,44 that Ga-doped titanates possess a high number of
oxygen vacancies and good oxide-ion conduction.
C. Electronic structure and phase diagram of 20% Ga- and
20% Nb-doped SrTiO3
Replacing another two Ti atoms with Ga atoms in 10%
Ga- and 20% Nb-doped SrTiO3 we obtain a model for 20%
Ga- and 20% Nb-doped SrTiO3 . The most stable structures
in this set of calculations have Ga atoms close to Nb atoms.
Up to three oxygen vacancies were generated in this structure
to study the effect of reducing conditions. It is preferable to
create the first two oxygen vacancies at the Ga–O–Ti bridge
where two vacancies share the same Ga atom forming a GaO4
unit, whereas the third oxygen vacancy is again positioned
at a Ga–O–Ti bridge forming a GaO5 unit (see supporting
information for the structures, Fig. S3).54
Constrained ab initio thermodynamic calculations of this
system were carried out to determine the phase stability at
various temperatures and oxygen partial pressures. In some
respects the phase transition of this system is quite similar to
that of the 10% Ga-doped system. In particular, the presence
of a reduced phase of both the 10 and 20% Ga-doped systems
occurs at approximately the same temperature and oxygen partial pressure range, indicating that increasing the concentration
of Ga does not significantly improve the reducibility of the
material. However, the phase diagram of the 20% Ga-doped
system shown in Fig. 8 displays no Sr-deficient phase (i.e.,
there are no SrO or TiO2 /Ga2 O3 /niobium oxide-rich second
phases). Furthermore, we observe from the DOS (Fig. 9)
a reduction in the electronic conductivity with increase in
Ga doping. As shown in Figs. 9(c) and 9(d), the DOS of
SrTi0.6 Nb0.2 Ga0.2 O2.9 and SrTi0.6 Nb0.2 Ga0.2 O2.85 exhibit only
two conduction electrons at the Fermi level. It seems that
doping with 20% Ga (and 20% Nb) and removing the first
oxygen atom in our supercell leads to a compensation of
the hole-doping effect of two Ga atoms and generation of
two conduction electrons from two uncompensated Nb atoms
at the Fermi level [Fig. 9(b)]. In contrast, removing one or
two more oxygen atoms from the supercell leads to localized
electrons observed in an extra peak in the DOS between
the valence and conduction band and no compensation of
the hole-doping effect of the remaining two Ga atoms, and
thus, no increase in charge carrier density [Figs. 9(c) and
9(d)]. Interestingly, creating a fourth oxygen vacancy under
very reducing conditions (usually not encountered in SOFC
operation and therefore not included in the phase diagram)
leads again to a full compensation of the hole-doping effect of
all four Ga atoms and generation of four conduction electrons
from the four Nb atoms at the Fermi level (see supporting
information, Fig. S4).54 Thus, while doping with 20% Ga
improves the ionic conductivity, the electronic conductivity
of the material is likely diminished under realistic fuel cell
operating conditions.
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PHYSICAL REVIEW B 84, 205102 (2011)
phase (SrTi0.8 Nb0.2 O3 ) at high temperature and low oxygen
partial pressure, which leads to a significant improvement
in electronic conductivity. This result is in excellent agreement with the defect chemistry model and experimental
observations reported by Kolodiazhnyi and Petric.28 Doping
20% Nb-doped SrTiO3 with 10% Ga enhances the ionic
conductivity of the material by creating oxygen vacancies.
The electronic conductivity is not reduced by small amounts
of Ga so that a mixed ionic/electronic conductor is formed.
However, doping with 20% Ga decreases the electronic conductivity of the material. This result supports the experimental
observations43,44 that doping with a small amount of Ga
improves the conductivity and promotes fast reduction of
the material. From both experimental observations and our
calculations, we propose that a mixed n-type and p-type
doping strategy could be a general approach to obtaining mixed ionic/electronic conductivity in perovskite oxide
materials.
ACKNOWLEDGMENTS
FIG. 9. Density of states of (a) SrTi0.6 Nb0.2 Ga0.2 O3 ,
(b) SrTi0.6 Nb0.2 Ga0.2 O2.95 , (c) SrTi0.6 Nb0.2 Ga0.2 O2.9 , and (d) SrTi0.6
Nb0.2 Ga0.2 O2.85 . Fermi energy is set to zero on the energy scale.
Numbers of electrons shown in the figure indicate the integrated
number of electrons per supercell for the specified DOS area, i.e.,
states in the band gap and states below the Fermi level.
IV. CONCLUSIONS
We have investigated the electronic properties and thermodynamic stability of Nb (n-type) and Ga (p-type) doped
SrTiO3 perovskites using DFT and constrained ab initio thermodynamic simulations. We find that cation vacancy compensated 20% Nb-doped Sr-deficient SrTiO3 (Sr0.9 Ti0.8 Nb0.2 O3 )
transforms to an electronically compensated non-Sr-deficient
*
Corresponding author:[email protected]
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